Suppose you are planning a house party for 9 people. You only want one type of drink in the party. You ask the guests to provide their preferences beforehand, and you store the data in a table:
Which drink should you serve?
There are actually multiple ways of answering this question:
Plurality Rule: Only considers how often each alternative is ranked in the first place. Hence, we would pick Gin tonic, as it has the most agents ranking it first (group A).
However, the majority (groups B and C combined) will probably be dissatisfied with this choice.
Condorcet method: Determine which alternative defeats every other alternative in pairwise majoirty comparisons:
Gin preferred to wine? 4 people
Beer preferred to wine? 3 people
Wine preferred to gin? 5 people
Wine preferred to beer? 6 people
Hence, we would pick Wine. Wine is called the Condorcet winner.
Single transferable vote (STV): eliminate the options that are ranked first by the lowest number of agents.
Remove wine from the choice set (first option of only 2 people)
Hence, we would pick Beer.
This simple example shows that collective choice is not a trivial matter. What method should I use? How to deal with ties? How to deal with manipulation?
Social choice theory is the set of methods for aggregating the preferences of multiple agents.
The Social choice theory originates from economics, political science, and mathematics. The considered ‘founders’ are:
Social theory as a scientific discipline: